Sacred geometry

Summary: Cultures have long imbued various spaces, shapes, forms, ratios, and geometric concepts with special significance and ritual power.

Humanity has long attributed sacred meaning to certain geometric forms and concepts. The term “sacred geometry” was popularized during the twentieth century to represent the religious, philosophical, and spiritual beliefs surrounding geometry. The core of its teachings may be found in very ancient cultures, with varying metaphysical systems and worldviews. Some attribute the modern renaissance of the movement to artist Jay Hambridge. The image of a nautilus shell with overlaid golden rectangles is common in the twenty-first century, but when Hambridge investigated mathematical proportion and symmetry in Greek art and architectural design in the beginning of the twentieth century, his work on dynamic symmetry led to debate about definitions of dynamic versus static symmetry.

The development of sacred geometry led to more debate as some asserted that it showed the continuity and universality of mathematical concepts or forms, such as the golden proportion, the logarithmic spiral, or the flower of life, across cultures, millennia, and the universe. In its most common conception, sacred geometry is then a metaphor for universal order—a metaphor found in the artistic expression of many cultures, especially in religious architecture. In its most ambitious conception, it is itself a practice for enlightenment or self-development, similar to meditation, prayer, or artistic techniques. The knowledge and exercise of geometrical skills can be taken to form a practice that awakens the practitioner to underlying order or truth. The movement has inspired its followers, who look for these forms in art, architecture, nature, and science. People like Drunvalo Melchizedek, who originally planned to major in physics and minor in mathematics but graduated with a fine arts degree, have organized spiritual workshops related to sacred geometry. Some attribute sacred geometry to people’s needs to seek out connections. Astrophysicist Mario Livio found some of the analyses “rather contrived… with lines drawn conveniently at points that are not obvious terminals at all. Furthermore, some of the ratios obtained are too convoluted… to be credible.”

Sacred diagrams and figures are omnipresent across ages and cultures. For example, the square has religious significance in Hindu architecture and design. The diagram known as the circular “mandala,” for instance, symbolizes to some the cosmos through its symmetry and sectors, which represent elements, seasons, divinities, and various categories of religious and metaphysical interest. Practitioners believe that meditating on The Flower of Life icon, one example of a mandala, will reveal the mysteries of the universe. The Egyptians used regular geometric polygons and pyramids in important architectural structures and in representations of the gods. Geometric figures, such as the platonic solids, were assigned additional significance in ancient Greece.

For instance, Earth was associated with the cube, air with the octahedron, water with the icosahedron, fire with the tetrahedron, and the dodecahedron was a model for the universe. In his work The Timeas, Plato noted: “So their combinations with themselves and with each other give rise to endless complexities, which anyone who is to give a likely account of reality must survey.” In the twentieth century, sacred geometry has become the universal language of nature, mastering shapes and patterns equally found in stars, snowflakes, and DNA, which ultimately represent a sort of blueprint of creation.

Golden Ratio

A common element in sacred geometry is the golden ratio. Many of the sacred geometry principles of the human body are found and subsumed into the famous “Vitruvian Man” drawing by Leonardo Da Vinci. “Vitruvian Man” was inspired by the work of Marcus Vitruvius Pollio, a first century Roman architect who wrote De architectura, or The Ten Books on Architecture. Vitruvius detailed systems of ratios he believed were found in the human body and that could be used to construct buildings, including temples, to achieve his three necessary criteria for structural perfection: beauty, durability, and utility. Da Vinci also lived and studied with the fifteenth-century mathematician Fra Luca Pacioli and drew the illustrations of the book De Divina Proportione (About Divine Proportion). In it, Pacioli explains and illustrates mathematical proportion in its direct relation of artistic patterns and forms and explores architecture and the vital proportion of the golden ratio, the ultimate divine proportion extensively.

Devotees of twentieth-century sacred geometry note the high occurrence of the golden ratio, such as its recursive occurrence in the Parthenon; the Notre Dame Cathedral; the great pyramid of Giza; the relations between platonic solids; the ratio of segments in a five-pointed star (called a pentagram); the ratio of adjacent terms of the famous Fibonacci Series, named after Leonardo Fibonacci; the symmetrical pattern of aperiodic tilings, thanks to which Roger Penrose discovered new aspects of quasicrystals; in movements of the stock market; and even in Erik Satie’s compositions.

Bibliography

Lawlor, Robert. Sacred Geometry: Philosophy & Practice. London: Thames & Hudson, 1982.

Livio, Mario. The Golden Ratio: The Story of PHI, the World’s Most Astonishing Number. New York: Broadway Books, 2003.

McWhinnie, H. J. “Influences of the Ideas of Jay Hambridge on Art and Design.” Journal of Computers & Mathematics with Applications 17, no. 4–6 (1989).

Skinner, Stephen. Sacred Geometry: Deciphering the Code. London: Gaia Books, 2006.